How can I see which edge connects to which when UV mapping?
You have 2 options in the UV editor, I guess you're looking for one of those:


Keep UV and object mesh in sync.
Automatically select the shared vertices.


You need to deactivate the first option to have access to the second. The first option keep a link between selected vertices in the 3D view mesh and the UV map selected vertices, second one only concerns the UV maps, but I maybe both will give what you want.